1. Field of the Invention
The present invention relates to imaging apparatuses and imaging methods, and more particularly relates to an imaging apparatus and an imaging method that forms an image of a subject by using Talbot interference.
2. Description of the Related Art
Imaging techniques that use interference of light with various wavelengths including visible light and X-rays have been known.
Known one of such imaging methods may be a Talbot interference method.
The Talbot interference method will be briefly described below. When a subject is irradiated with light, the phase of the light is changed when the light is transmitted through the subject. When this light is emitted on a first grating (diffraction grating) having a specific pattern, the light diffracted by the first grating makes interference at a constant distance and forms an interference pattern called self image. When the self image is analyzed, information relating to the phase of the subject can be obtained.
Also, referring to the specification of U.S. Pat. No. 5,812,629, a shield grating including shielding portions that shield light and transmissive portions that transmit light is arranged at a position at which a self image is formed. By shielding part of the self image, a Moiré is formed.
If the described method, in which the Moiré is formed by using the self image and the Moiré is detected, is used, information relating to the phase of the subject can be obtained by using a detector with a resolution larger than the period of the self image.
Typically, when X-rays are used as light, the period of the self image is smaller than the resolution of the detector. Hence, the method of forming the Moiré is particularly effective when the X-rays are used as the light as described in U.S. Pat. No. 5,812,629. In an imaging apparatus described in U.S. Pat. No. 5,812,629, a second grating (shield grating) including the shielding portions that shield the light and the transmissive portions that transmit the light is arranged at the position at which the self image is formed. By shielding part of the self image, the Moiré is formed.
Several kinds of methods exist for generating the Moiré by using the second grating.
For example, there is a method of using a second grating having the same shape and period as the shape and period of the self image. By slightly rotating the angle of the second grating, a Moiré with high legibility is obtained.
For another example, there is a method of using a second grating having a period slightly different from the period of the self image. In either case, the self image is enhanced by the Moiré.
Also, several kinds of methods exist for calculating a change in wavefront shape of light due to a subject, from a displacement of a Moiré.
One of such methods is a method of analyzing the period of a Moiré by using a wave number space. Specifically, the Fourier transform and wavelet transform may be exemplified. It is to be noted that the Fourier transform contains the Fourier transform with a window function in this specification. M. Takeda, H. Ina, and S. Kobayashi, J. Opt. Soc. Am. 72, 156-160 (1982) describes a method of performing the Fourier transform for a Moiré by using the Fourier transform method, and extracting and analyzing a Moiré component in the wave number space. The principle of this method will be briefly described below. First, spatial frequency spectra are obtained by performing the Fourier transform for the detection result. Next, a spectrum with the frequency of a basic period component of the Moiré (hereinafter, referred to as carrier frequency) and an area around that spectrum are extracted, and are moved to an origin. The inverse Fourier transform is performed for this frequency spectrum to obtain a differential phase image of the subject, and the differential phase image is integrated to obtain a phase image of the subject.
The technique disclosed by M. Takeda, H. Ina, and S. Kobayashi, J. Opt. Soc. Am. 72, 156-160 (1982) is the one-dimensional Fourier transform method. With this transform method, a two-dimensional differential phase image cannot be obtained.
Owing to this, a first grating having a two-dimensional structure is used in a Talbot interferometer, to form a self image having a two-dimensional pattern. Then, a second grating having a proper shape corresponding to the self image is provided, and hence a two-dimensional Moiré can appear.
However, if the period of the Moiré is analyzed by using the wave number space, the accuracy for retrieval of the phase of light may vary depending on the shape of the Moiré.
In particular, when the phase is retrieved by the method of analyzing the period of the Moiré by using the wave number space, a satisfactory result may not be obtained depending on the combination of the first and second gratings.